fem_check22_la.c running 
Given uxx + 2 uxy + 3 uyy + 4 ux + 5 uy + 6 u = 
6x^3+6y^3+12x^2+15y^2+6xy+11x+22y+8 
xmin<=x<=xmax ymin<=y<=ymax Boundaries 
Analytic solution u(x,y) =  x^3 + y^3 +xy + 1 
xmin=0, xmax=1, ymin=0, ymax=1 
nx=4, ny=4 
x grid and analytic solution at ymin 
i=0, Ua( 0.000)= 1.000 
i=1, Ua( 0.333)= 1.037 
i=2, Ua( 0.667)= 1.296 
i=3, Ua( 1.000)= 2.000 

y grid and analytic solution at xmin
ii=0, Ua( 0.000)= 1.000 
ii=1, Ua( 0.333)= 1.037 
ii=2, Ua( 0.667)= 1.296 
ii=3, Ua( 1.000)= 2.000 

solution at i=0,x=0, ii=0,y=0 is 1 
solution at i=0,x=0, ii=1,y=0.333333 is 1.03704 
solution at i=0,x=0, ii=2,y=0.666667 is 1.2963 
solution at i=0,x=0, ii=3,y=1 is 2 
solution at i=1,x=0.333333, ii=0,y=0 is 1.03704 
solution at i=1,x=0.333333, ii=1,y=0.333333 is 1.18519 
solution at i=1,x=0.333333, ii=2,y=0.666667 is 1.55556 
solution at i=1,x=0.333333, ii=3,y=1 is 2.37037 
solution at i=2,x=0.666667, ii=0,y=0 is 1.2963 
solution at i=2,x=0.666667, ii=1,y=0.333333 is 1.55556 
solution at i=2,x=0.666667, ii=2,y=0.666667 is 2.03704 
solution at i=2,x=0.666667, ii=3,y=1 is 2.96296 
solution at i=3,x=1, ii=0,y=0 is 2 
solution at i=3,x=1, ii=1,y=0.333333 is 2.37037 
solution at i=3,x=1, ii=2,y=0.666667 is 2.96296 
solution at i=3,x=1, ii=3,y=1 is 4 

boundary i=0,x=0, ii=0,y=0 is 1 
boundary i=0,x=0, ii=3,y=1 is 2 
boundary i=1,x=0.333333, ii=0,y=0 is 1.03704 
boundary i=1,x=0.333333, ii=3,y=1 is 2.37037 
boundary i=2,x=0.666667, ii=0,y=0 is 1.2963 
boundary i=2,x=0.666667, ii=3,y=1 is 2.96296 
boundary i=3,x=1, ii=0,y=0 is 2 
boundary i=3,x=1, ii=3,y=1 is 4 
boundary i=0,x=0, ii=0,y=0 is 1 
boundary i=3,x=1, ii=0,y=0 is 2 
boundary i=0,x=0, ii=1,y=0.333333 is 1.03704 
boundary i=3,x=1, ii=1,y=0.333333 is 2.37037 
boundary i=0,x=0, ii=2,y=0.666667 is 1.2963 
boundary i=3,x=1, ii=2,y=0.666667 is 2.96296 
boundary i=0,x=0, ii=3,y=1 is 2 
boundary i=3,x=1, ii=3,y=1 is 4 
calling gauleg xmin=0, xmax=1, npx=12 
calling gauleg ymin=0, ymax=1, npy=12 
xx[1]=0.00921968, xx[2]=0.0479414, wx[1]=0.0235877, wx[2]=0.0534697 
yy[1]=0.00921968, yy[2]=0.0479414, wy[1]=0.0235877, wy[2]=0.0534697 
galk(xx[2],yy[2])=8.45583 
galf(xx[2],yy[2])=1.40396 
compute stiffness matrix 
Legendre integration=1.77202, at i=1, j=0, ii=1, jj=0 
Legendre integration=-1.04969, at i=1, j=0, ii=1, jj=1 
Legendre integration=0.0606983, at i=1, j=0, ii=1, jj=2 
Legendre integration=0.0526913, at i=1, j=0, ii=1, jj=3 
Legendre integration=-0.625523, at i=1, j=0, ii=2, jj=0 
Legendre integration=2.34967, at i=1, j=0, ii=2, jj=1 
Legendre integration=-1.04969, at i=1, j=0, ii=2, jj=2 
Legendre integration=0.16126, at i=1, j=0, ii=2, jj=3 
Legendre integration=3.59334, at i=1, j=1, ii=1, jj=0 
Legendre integration=-15.7702, at i=1, j=1, ii=1, jj=1 
Legendre integration=10.9536, at i=1, j=1, ii=1, jj=2 
Legendre integration=-1.95888, at i=1, j=1, ii=1, jj=3 
Legendre integration=-0.801735, at i=1, j=1, ii=2, jj=0 
Legendre integration=7.04824, at i=1, j=1, ii=2, jj=1 
Legendre integration=-15.7702, at i=1, j=1, ii=2, jj=2 
Legendre integration=6.34156, at i=1, j=1, ii=2, jj=3 
Legendre integration=-1.29533, at i=1, j=2, ii=1, jj=0 
Legendre integration=5.87663, at i=1, j=2, ii=1, jj=1 
Legendre integration=0.192943, at i=1, j=2, ii=1, jj=2 
Legendre integration=-0.579605, at i=1, j=2, ii=1, jj=3 
Legendre integration=0.490753, at i=1, j=2, ii=2, jj=0 
Legendre integration=-3.41951, at i=1, j=2, ii=2, jj=1 
Legendre integration=5.87663, at i=1, j=2, ii=2, jj=2 
Legendre integration=1.24677, at i=1, j=2, ii=2, jj=3 
Legendre integration=0.0422449, at i=1, j=3, ii=1, jj=0 
Legendre integration=-0.338878, at i=1, j=3, ii=1, jj=1 
Legendre integration=-1.06416, at i=1, j=3, ii=1, jj=2 
Legendre integration=0.356327, at i=1, j=3, ii=1, jj=3 
Legendre integration=-0.0679592, at i=1, j=3, ii=2, jj=0 
Legendre integration=0.367806, at i=1, j=3, ii=2, jj=1 
Legendre integration=-0.338878, at i=1, j=3, ii=2, jj=2 
Legendre integration=-0.965434, at i=1, j=3, ii=2, jj=3 
Legendre integration=-0.671327, at i=2, j=0, ii=1, jj=0 
Legendre integration=0.586837, at i=2, j=0, ii=1, jj=1 
Legendre integration=0.0351276, at i=2, j=0, ii=1, jj=2 
Legendre integration=-0.055102, at i=2, j=0, ii=1, jj=3 
Legendre integration=0.240612, at i=2, j=0, ii=2, jj=0 
Legendre integration=-0.962908, at i=2, j=0, ii=2, jj=1 
Legendre integration=0.586837, at i=2, j=0, ii=2, jj=2 
Legendre integration=0.0309949, at i=2, j=0, ii=2, jj=3 
Legendre integration=1.11298, at i=2, j=1, ii=1, jj=0 
Legendre integration=2.75235, at i=2, j=1, ii=1, jj=1 
Legendre integration=-3.51715, at i=2, j=1, ii=1, jj=2 
Legendre integration=0.808967, at i=2, j=1, ii=1, jj=3 
Legendre integration=-0.550676, at i=2, j=1, ii=2, jj=0 
Legendre integration=1.07165, at i=2, j=1, ii=2, jj=1 
Legendre integration=2.75235, at i=2, j=1, ii=2, jj=2 
Legendre integration=-2.11618, at i=2, j=1, ii=2, jj=3 
Legendre integration=3.59334, at i=2, j=2, ii=1, jj=0 
Legendre integration=-15.7702, at i=2, j=2, ii=1, jj=1 
Legendre integration=10.9536, at i=2, j=2, ii=1, jj=2 
Legendre integration=-1.95888, at i=2, j=2, ii=1, jj=3 
Legendre integration=-0.801735, at i=2, j=2, ii=2, jj=0 
Legendre integration=7.04824, at i=2, j=2, ii=2, jj=1 
Legendre integration=-15.7702, at i=2, j=2, ii=2, jj=2 
Legendre integration=6.34156, at i=2, j=2, ii=2, jj=3 
Legendre integration=0.0772864, at i=2, j=3, ii=1, jj=0 
Legendre integration=1.14888, at i=2, j=3, ii=1, jj=1 
Legendre integration=2.6715, at i=2, j=3, ii=1, jj=2 
Legendre integration=-0.924452, at i=2, j=3, ii=1, jj=3 
Legendre integration=0.107334, at i=2, j=3, ii=2, jj=0 
Legendre integration=-0.810775, at i=2, j=3, ii=2, jj=1 
Legendre integration=1.14888, at i=2, j=3, ii=2, jj=2 
Legendre integration=2.52778, at i=2, j=3, ii=2, jj=3 
Legendre integration=1.99045, f at i=1, ii=1 
Legendre integration=5.6475, f at i=1, ii=2 
Legendre integration=4.46625, f at i=2, ii=1 
Legendre integration=8.42705, f at i=2, ii=2 
k computed stiffness matrix, see above 
f computed forcing function, see above 
ug computed Galerkin, Ua analytic, error 
ug[0,0]= 1.000, Ua= 1.000, err=1.33227e-15 
ug[0,1]= 1.037, Ua= 1.037, err=0 
ug[0,2]= 1.296, Ua= 1.296, err=0 
ug[0,3]= 2.000, Ua= 2.000, err=0 
ug[1,0]= 1.037, Ua= 1.037, err=8.88178e-16 
ug[1,1]= 1.185, Ua= 1.185, err=-2.22045e-15 
ug[1,2]= 1.556, Ua= 1.556, err=-2.66454e-15 
ug[1,3]= 2.370, Ua= 2.370, err=0 
ug[2,0]= 1.296, Ua= 1.296, err=0 
ug[2,1]= 1.556, Ua= 1.556, err=-1.9984e-15 
ug[2,2]= 2.037, Ua= 2.037, err=-1.33227e-15 
ug[2,3]= 2.963, Ua= 2.963, err=0 
ug[3,0]= 2.000, Ua= 2.000, err=0 
ug[3,1]= 2.370, Ua= 2.370, err=0 
ug[3,2]= 2.963, Ua= 2.963, err=0 
ug[3,3]= 4.000, Ua= 4.000, err=0 
                                        maxerr=2.66454e-15, avgerr=6.52256e-16